In the oil and gas industry seismic trace data (S{t}) is generally modelled as a seismic wavelet (W{t}) convolved with a reflection coefficient sequence (R{t}) plus an additive noise component (N{t}). It can be written as follows: (1) S{t}=W{t}*R{t}+N{t}, where * represents convolution.
The desired result of the seismic investigation process is to obtain the best estimate of the reflection coefficients. When complex wavelets are present on the trace records it causes the interpretation (i.e. estimate of the principle characteristics of the reflection coefficient sequence) of the seismic data to be difficult. Subsequent inversion of the seismic data to an impedance or reflectivity estimate is similarly difficult or impossible.
Deconvolution, to reduce the wavelet to a simple, known and desirable form, is routinely applied during the digital processing of the seismic data. A considerable body of research and publications clearly documents the methods currently available. They include statistical methods based on the minimum phase assumption such as the Wiener-Levinson method, the sparse spike assumption, homomorphic methods and others. These methods all have some success but in general also have some deficiencies under various conditions.
Where well control exists, matching filters between the well data and the processed and stacked seismic data are sometimes derived at the projected locations of that well control onto the seismic line or volume. The matching filter, in some circumstances, can reduce the wavelet to its desired form at the well location but is only valid at that specific location and does not address lateral changes occurring in the wavelet.